Place peas, garlic, salt, kale, and lemon juice into a food processor. Pulse a few times until everything is coarsely chopped.
While the food processor is running, slowly stream in olive oil and blend until everything is incorporated into a smooth pesto. Scrape down the sides of the food processor with a spatula and pulse once more to incorporate.
Serve immediately or store pesto in an airtight container in the fridge for up to a week. This pesto also freezes beautifully if you want to keep it longer!